# Modules

## Core modules

### Semester 1

- Algebraic Topology
- Asymptotic and Analytical Methods
- Continuum Mechanics
- Dynamical Systems and Conservation Laws
- Foundations of Probability
- Groups, Rings and Modules
- Measure and Integration
- Regression and Simulation Methods

### Semester 2

- Algebras and Representation Theory
- Elliptic and Parabolic PDEs
- Functional Analysis
- Manifolds
- Mathematical Biology and Physiology
- Modern Regression and Bayesian Methods
- Numerical Methods
- Stochastic Processes

## Supplementary modules

### Semester 1

### Semester 2

- Classical and Quantum Integrable Systems
- Homological Algebra
- Finite Element Methods for PDEs
- Data Science for Dynamical Systems

### Previous supplementary modules

These modules ran previously, and are not currently running in this session.

- Advanced PDE I
- Advanced PDE II
- Algebraic Statistics
- Calculus of Variations and Dynamics
- Combinatorics on Words
- Convergence of Probability Measures and its Applications
- Finance, Risk, Asset-Pricing, Credit Scoring etc.
- Formal Groups
- Fourier and Harmonic Analysis
- Galois Theory of Commutative Rings
- History of Mathematics
- Introduction to Geometric Group Theory
- Inverse Problems
- Mathematical Foundations of Elasticity Theory
- Stochastic Networks and Processes
- Stochastic PDEs: Applications and Numerics
- Variational methods for PDEs and nonlocal problems